Solar Eclipse on Neptune (Refer to Exercise 69.) The sun's distance from Neptune is approximately 2,800,000,000 mi (2.8 billion mi). The largest moon of Neptune is Triton, with a diameter of approximately 1680 mi. (Data fromThe World Almanac and Book of Facts.) b. Triton is approximately 220,000 mi from Neptune. Is it possible for Triton to cause a total eclipse on Neptune?

Verified step by step guidance

1. insert step 1: Understand the concept of a total eclipse. A total eclipse occurs when a celestial body completely covers the light from a source, such as the sun.
2. insert step 2: Calculate the angular diameter of the sun as seen from Neptune. Use the formula for angular diameter: \( \theta = 2 \times \arctan\left(\frac{d}{2D}\right) \), where \( d \) is the diameter of the sun and \( D \) is the distance from Neptune to the sun.
3. insert step 3: Calculate the angular diameter of Triton as seen from Neptune. Use the same formula for angular diameter: \( \theta = 2 \times \arctan\left(\frac{d}{2D}\right) \), where \( d \) is the diameter of Triton and \( D \) is the distance from Neptune to Triton.
4. insert step 4: Compare the angular diameters of the sun and Triton. For a total eclipse to occur, Triton's angular diameter must be greater than or equal to the sun's angular diameter as seen from Neptune.
5. insert step 5: Conclude whether a total eclipse is possible based on the comparison of angular diameters. If Triton's angular diameter is greater, a total eclipse is possible; otherwise, it is not.

Key Concepts

Angular Size

Angular size refers to how large an object appears to an observer from a given distance. It is determined by the object's actual size and its distance from the observer. In the context of eclipses, the angular size of the moon (Triton) relative to the sun is crucial in determining whether it can completely cover the sun when viewed from Neptune.

Eclipse Geometry

Eclipse geometry involves the spatial arrangement of the sun, moon, and planet during an eclipse. For a total eclipse to occur, the moon must be directly between the sun and the planet, with the moon's angular size being equal to or greater than that of the sun as seen from the planet. Understanding this geometry helps in assessing the conditions under which Triton could cause a total eclipse on Neptune.

Distance and Scale

Distance and scale are fundamental in understanding celestial events. The vast distances between celestial bodies, such as the sun, Neptune, and Triton, affect their apparent sizes and the likelihood of eclipses. In this scenario, calculating the distances involved helps determine if Triton is sufficiently large and close enough to Neptune to block the sun's light entirely.